Write the slope-intercept form of the equation of the line passing through the point (5,1) and parallel to the line y=-4x-2.
To find the equation of a line parallel to a given line, we need to use the fact that parallel lines have the same slope.
The given line has a slope of -4. Since the line we are looking for is parallel to this line, it will also have a slope of -4.
We can use the point-slope form of a line to find the equation. The point-slope form is y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope.
Given point: (5, 1)
Slope: -4
Substituting the values into the point-slope form:
y - 1 = -4(x - 5)
Now, let's simplify the equation to its slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
First, distribute -4 to the terms in parentheses:
y - 1 = -4x + 20
Next, add 1 to both sides of the equation to isolate y:
y = -4x + 21
Therefore, the slope-intercept form of the equation for the line passing through the point (5, 1) and parallel to the line y = -4x - 2 is y = -4x + 21.